The way a simple virus invades a cell is with double stranded DNA replication. The virus has a coat of protein covering the DNA, once bound to the side of the cell the virus releases the DNA where it is then replicated and transcribed into RNA and translated into more proteins. These proteins and DNA replicas are then combined into particles and the process repeats. Over time the cell will fill with these particles and eventually burst, this is called cell lysis. The new particles are released into the body to further invade and replicate in new cells.
HIV is a retrovirus that reverses the normal flow of genetic information. The virus has an envelope as well as a protein coat but instead of double stranded DNA it contains RNA and teh enzyme reverse transcriptase. This enzyme transcribes the RNA into DNA and then forms another DNA strand to make a double stranded helix. This DNA strand is then integrated into the DNA of the cell. The cell then transcribes the DNA into RNA and translates int RNA into more reverse transcriptase and envelop and coat proteins. The new HIV particles are then assembled ready to invade more cells.